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Simplifying 2528x2 + -2528x + 631 = 0 Reorder the terms: 631 + -2528x + 2528x2 = 0 Solving 631 + -2528x + 2528x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2528 the coefficient of the squared term: Divide each side by '2528'. 0.2496044304 + -1x + x2 = 0 Move the constant term to the right: Add '-0.2496044304' to each side of the equation. 0.2496044304 + -1x + -0.2496044304 + x2 = 0 + -0.2496044304 Reorder the terms: 0.2496044304 + -0.2496044304 + -1x + x2 = 0 + -0.2496044304 Combine like terms: 0.2496044304 + -0.2496044304 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.2496044304 -1x + x2 = 0 + -0.2496044304 Combine like terms: 0 + -0.2496044304 = -0.2496044304 -1x + x2 = -0.2496044304 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.2496044304 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.2496044304 + 0.25 Combine like terms: -0.2496044304 + 0.25 = 0.0003955696 0.25 + -1x + x2 = 0.0003955696 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0003955696 Calculate the square root of the right side: 0.019888932 Break this problem into two subproblems by setting (x + -0.5) equal to 0.019888932 and -0.019888932.Subproblem 1
x + -0.5 = 0.019888932 Simplifying x + -0.5 = 0.019888932 Reorder the terms: -0.5 + x = 0.019888932 Solving -0.5 + x = 0.019888932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.019888932 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.019888932 + 0.5 x = 0.019888932 + 0.5 Combine like terms: 0.019888932 + 0.5 = 0.519888932 x = 0.519888932 Simplifying x = 0.519888932Subproblem 2
x + -0.5 = -0.019888932 Simplifying x + -0.5 = -0.019888932 Reorder the terms: -0.5 + x = -0.019888932 Solving -0.5 + x = -0.019888932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.019888932 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.019888932 + 0.5 x = -0.019888932 + 0.5 Combine like terms: -0.019888932 + 0.5 = 0.480111068 x = 0.480111068 Simplifying x = 0.480111068Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.519888932, 0.480111068}
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